Granular Magnetic Systems Research Articles

Models of advanced recording systems: A multi-timescale micromagnetic code for granular thin film magnetic recording systems

Micromagnetic modelling provides the ability to simulate large magnetic systems reliably without the computational cost limitation imposed by atomistic modelling. Through micromagnetic modelling it is possible to simulate systems consisting of thousands of grains over a time range of nanoseconds to years, depending upon the solver used. Here we present the creation and release of an open-source multi-timescale micromagnetic code combining three key solvers: Landau-Lifshitz-Gilbert; Landau-Lifshitz-Bloch; Kinetic Monte Carlo. This code, called MARS (Models of Advanced Recording Systems), is capable of accurately simulating the magnetisation dynamics in large and structurally complex single- and multi-layered granular systems as is shown by comparison to established atomistic simulation results. The short timescale simulations are achieved for systems far from and close to the Curie point via the implemented Landau-Lifshitz-Gilbert and Landau-Lifshitz-Bloch solvers respectively. This enables read/write simulations for general perpendicular magnetic recording and also state of the art heat assisted magnetic recording (HAMR). The long timescale behaviour is simulated via the Kinetic Monte Carlo solver, enabling investigations into signal-to-noise ratio and data longevity. The combination of these solvers opens up the possibility of multi-timescale simulations within a single software package. For example the entire HAMR process from initial data writing and data read back to long term data storage is possible via a single simulation using MARS. The use of atomistic parameterisation for the material input of MARS enables highly accurate material descriptions which provide a bridge between atomistic simulation and real world experimentation. Thus MARS is capable of performing simulations for all aspects of recording media research and development. This ranges from material characterisation and optimisation to system design and implementation. The object orientated nature of MARS is structured to facilitate quick and simple development and easy implementation of user defined custom simulation types which can utilise either timescale or a combination of both timescales. Program summaryProgram title: MARSCPC Library link to program files:https://doi.org/10.17632/8mx7cndcdx.1Developer's repository link:https://bitbucket.org/EwanRannala/mars/Code Ocean capsule:https://codeocean.com/capsule/2549929Licensing provisions: MITProgramming language: C++Supplementary material: MARS testing methodology (PDF), HAMR simulation example video.Nature of problem: A combined model that enables the complete modelling of magnetic recording processes at elevated temperatures covering all time scales from writing (nanoseconds) up to long term data storage (years). The model must also accurately describe the granular nature of the recording media as grain sizes are reduced to a few nanometres.Solution method: Short timescale behaviours are captured via the Landau-Lifshitz-Gilbert and Landau-Lifshitz-Bloch solvers for low and high temperature systems respectively. The long time scale behaviours are captured via a kinetic Monte Carlo solver. To enable complex models which account for mixed timescale behaviours the solvers are implemented as a single class structure which allows for dynamic solver selection. The granular structure is generated via a Laguerre-Voronoi tessellation with a custom implemented packing algorithm to produce highly realistic grain size distributions. Complex thermal dependencies of materials can be incorporated via atomistic parameterisation forming a multi-timescale model of the material.

Interfacial Roughness Facilitated by Dislocation and a Metal-Fuse Resistor Fabricated Using a Nanomanipulator.

Granular magnetic systems consisting of magnetic nanoparticles embedded in a nonmagnetic metallic matrix have emerged as an attractive building block for nanodevices. A key challenge for building interface-based nanodevice applications, such as magnetic memory devices, is to clearly know about the influences of interfacial roughness on the scattering of conduction electrons. Here, we demonstrate a granular magnetic system composed of Co and Cu nanoparticles and further link the atomic structure of the Co/Cu interface to the scattering mechanism of conduction electrons. The multiple scattering is caused by the dislocations at the rough interface, which lead to a reduction of conduction efficiency and an increase of energy consumption. These dislocations mostly originate from the lattice defects on the surface of nanoparticles, the lattice mismatch of two crystal structures, and the different surface energies. Based on the negative effects of a rough interface on electronic transport, we first develop a nanometal-fuse resistor, which could hopefully be used in the protection circuits of nanodevices. Our results may open up the possibility of implementing the low-dimensional granular magnetic materials in nanodevice applications.

A Particle Coupling Finite Element Method for Shock-Mitigation Characterization of Magnetic Granular Systems

Granular chain system could realize the impulse protection mechanism. This work presents the shock mitigation characteristics of magnetic granular chains in different configurations. Based on magneto-structural coupling algorithm, a particle coupling finite element method is proposed. The coupling process is to numerically capture the process of the pre-compression and magnetic force of each grain in magnetic analysis and the field-induced dynamic responses under impulse loadings. For validation, an experimental set-up is designed, and the experimental results are tested and compared. The numerical predicted values present a good agreement with experimental results. It is shown that, when the characteristics of peak force, peak velocity, incident kinetic energy and stress wave propagation are compared, the performance in interstitial decorated chains is superior and followed by reverse-interstitial decorated chains and then monodisperse chain. The increment of magnetic field strength enhances the field-induced pre-compression, magnetic force, and shock mitigation capacity of granular chains. Such nonlinear behavior of magnetic granular chains can be exploited in order to design new tunable devise, such as shock absorbers and impulse protector.

Features of ferromagnetic resonance in nanogranule (CoFeB) m С100 − m structures

The magnetoresonance characteristics of granular nanocomposite magnetic systems with carbon matrices are studied. Analysis of the experimental data reveals the formation of iron/cobalt carbide nanoparticles upon synthesis that determine the magnetoresonance characteristics.

Magnetic avalanches in granular ferromagnets: thermal activated collective behavior

We present a numerical study on the thermal activated avalanche dynamics in granular materials composed of ferromagnetic clusters embedded in a non-magnetic matrix. A microscopic dynamical simulation based on the reaction-diffusion process is developed to model the magnetization process of such systems. The large-scale simulations presented here explicitly demonstrate inter-granular collective behavior induced by thermal activation of spin tunneling. In particular, we observe an intriguing criticality controlled by the rate of energy dissipation. We show that thermal activated avalanches can be understood in the framework of continuum percolation and the emergent dissipation induced criticality is in the universality class of 3D percolation transition. Implications of these results to the phase-separated states of colossal magnetoresistance materials and other artificial granular magnetic systems are also discussed.

Minor loop analysis using Monte Carlo simulation for clusters with various magnetic site densities

Magnetic granular systems have been applied to many fields of study, e.g. spin glass properties or magnetic resistance phenomena. These magnetic granular systems have homogeneous densities of magnetic granules and there physical properties changes depending on its densities. In this study, to investigate magnetic properties of such granular systems, minor loop analysis was performed using Monte Carlo simulation. As the granular systems, clusters with various magnetic site densities were constructed by simple diffusion model. Moreover, these clusters were analyzed from new point of view which is a concept of a “colony”. The results of minor loop analysis were considered associating with colony.

Interaction effects on the coercivity and fluctuation field in granular powder magnetic systems

In this paper, the interaction effects on the coercivity ( H c) and Fluctuation fields ( H f) of doped barium–ferrite particles at different concentrations are examined. Samples with different concentrations are prepared by mixing the original powder with a non-magnetic host. Coercivity measurements at different particle concentrations showed that for high concentrations, the coercivity decreases with decreasing particle concentration. This attributed to the reduction of positive dipolar interactions that arise from stacking effects. However, at very low concentrations, H c is observed to increase with decreasing concentration due to the reduction in the predominant negative dipolar interactions. Measurements of fluctuation field using the waiting time technique show that the behavior of H f at different concentrations is greatly influenced by particle interactions. This result can be understood since H f is governed by the distribution of effective energy barriers F(Δ E eff).

Dynamic relaxation of magnetic clusters in a ferromagnetic(Ga,Mn)Asepilayer

A scenario of the mechanism of intriguing ferromagnetic properties in Mn-doped magnetic semiconductor $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$ is examined in detail. We find that magnetic features seen in zero-field-cooled and field-cooled magnetizations are not interpreted with a single domain model [Phys. Rev. Lett. 95, 217204 (2005)], and the magnetic relaxation, which is similar to that seen in magnetic particles and granular systems, is becoming significant at temperatures above the lower-temperature peak in the temperature dependence of ac susceptibility, supporting the cluster/matrix model reported in our previous work [Phys. Rev. Lett. 94, 147203 (2005)]. Cole-Cole analysis reveals that magnetic interactions between such $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$ clusters are significant at temperatures below the higher-temperature peak in the temperature dependent ac susceptibility. The magnetizations of these films disappear above the temperature showing the higher-temperature peak, which is generally referred to as the Curie temperature. However, we suggest that these combined results are evidence that the temperature is actually the blocking temperature of $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$ clusters with a relatively high hole concentration compared to the $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$ matrix.

Modeling of long-time thermal magnetization decay in interacting granular magnetic materials

We present a general method to evaluate the long-time magnetization decay in granular magnetic systems. The method is based on Arrhenius-Neel kinetics with the evaluation of the energy barriers in a multidimensional space. To establish a possible reversal mode, we suggest the use of Metropolis Monte Carlo and for the mode statistical sampling-the kinetic Monte Carlo criteria. The examples considered include long-time magnetization decay in CoCrPt low-magnetization longitudinal recording media and in a collection of Co particles with different concentrations.

Interaction effects in magnetic granular systems

Interactions in magnetic granular systems are difficult to address in real systems. Several experimental results have been obtained along the last 50 years, but few theoretical approaches have been developed to account for these extremely complex systems. A brief review on the role of interactions on the magnetic properties of granular magnetic systems is given, with a focus on a novel approach known as interacting superparamagnetic model. Two different systems are tested, and the results are discussed in terms of such phenomenological model.

Inverse tunnel magnetoresistance associated with Coulomb staircases in micro-fabricated granular systems

Abstract We have investigated spin-dependent single-electron tunneling (SET) in micro-fabricated magnetic granular systems with current-perpendicular-to-plane geometry. Electron beam lithography technique and Ar ion etching were employed for the micro-fabrication process to form a Co/Al-O/Co 31 Al 24 O 45 /Co/Pt pillar with the cross section of 0.4×0.4 μm 2 . Inverse tunnel magnetoresistance is observed around the step-up points of Coulomb staircases. The observed results are beyond the orthodox theory of SET for a double junction model without spin-accumulation effects.

Random walk simulation of magnetotransport in magnetic granular systems

An integral series for the conductivity of magnetic inhomogeneous systems was previously derived from the real-space Kubo formula and semiclassical Boltzmann equation independently. In this work, we show that the integral series can be evaluated by using a random-walk sampling technique. The approach is applied first to a simple nonmagnetic single-granule system, and then to the giant magnetoresistance (GMR) effect of magnetic granular systems. It is well suitable for the granular systems in which the granular size is smaller than the electron mean free path, where the macroscopic approach becomes invalid. The GMR is found to always increase with decreasing size of granules. Optimum GMR could be obtained by a proper adjustment of the spin-dependent scattering strengths due to interfacial roughness and bulk impurities.

Fe–Ag magnetic granular systems: a SANS study with polarised neutrons

We present small angle scattering measurements performed on Fe–Ag granular systems using polarised neutrons. Various samples with different iron concentration have been investigated and the analysis of the experimental data points out that samples morphology does not change remarkably with Fe content. Finally, the study of the polarised signal indicates the presence of Fe rich regions in the nanometer range of size having a negligible magnetisation.

Small-angle neutron scattering measurements with polarised neutrons on Fe–Ag magnetic granular systems

Different Fe-Ag magnetic granular samples have been prepared by changing the relative Fe volume concentration. The evolution of their morphology with iron concentration has been studied by small angle scattering measurements performed with polarised neutrons. The particles average size determined from nuclear scattering data is about 7 Å and it does not change with varying Fe content. On the other hand, the shapes of nuclear and magnetic scattering curves are different in the range of sizes corresponding to magnetic particles, indicating that similar structures display different magnetic behaviours. Finally, the analysis of polarised neutron data suggests the existence of Fe rich regions with negligible magnetisation.

Fluctuation fields and reversal mechanisms in granular magnetic systems

In this paper, the behaviour of the fluctuation of the fluctuation field ( H f) and its relationship with the activation energy for reversal in magnetic systems is examined. At a constant level of magnetisation, the link between thermal energy and field induced changes in the magnetisation of the system using different forms of the equation of state are found to give the same value of H f. Accordingly, the former S/ χ irr and the ∂H/ ∂ln( M ̇ irr )| M irr techniques for determining H f are found to be consistent so long as the analysis of H f is made at the same constant level of irreversible magnetisation ( M irr). Both techniques show that the fluctuation field can be determined using H f=Δ H/Δln( t)| M irr which is more accessible to experiment. Hence, one can define H f as the change in field required to maintain the magnetisation of the system unchanged during a time interval of Δln( t)=1. The behaviour of the fluctuation field in systems that contain a distribution of activation energies ( f(Δ E)) is found to be governed by the nature of f(Δ E). For the case where this distribution arises from distributions of both particle volumes and anisotropy fields, the variation of H f with M irr is predicted to be approximately constant when both distributions have comparable standard deviations. Also H f is predicted to be constant with M irr is the case where both distributions become extremely narrow (i.e. the case of a single activation energy). Hence H f remaining constant with M irr cannot be used to show that the activation energy in the system is constant. In addition if the system contains a single activation energy, a constant value of H f cannot be used to distinguish between reversal mechanisms such as coherent rotation or weak domain wall pinning.

Temperature behavior of anhysteretic magnetization in granular magnetic systems

Temperature measurements of the anhysteretic magnetization M were performed on nearly-superparamagnetic, granular Cu 90Co 10 submitted to different Joule-heating currents using a VSM. Below about 500 K, the anhysteretic magnetization is fully reversible. All isothermal M( H) curves may be fitted by a superposition of Langevin functions with distributed magnetic moments; however, the reduced magnetization M/ M s is not observed to scale with H/ T; on the contrary, all curves are nearly exactly coincident when plotted against M s/ T. This result is phenomenologically interpreted in terms of an apparent average magnetic moment linearly growing with the ratio T/ M s.

Observation of isotropic giant magnetoresistance in paramagneticAu80Fe20

Magnetization and magnetoresistance were measured at room temperature and above on ${\mathrm{Au}}_{80}{\mathrm{Fe}}_{20}$ platelets and ribbons obtained by solid-state quenching and melt spinning. The as-quenched samples contain a solid solution of Fe in Au and exhibit a paramagnetic (Curie-Weiss) behavior in the considered temperature range; magnetic data indicate very short-ranged magnetic correlation among adjacent spins, enhanced by local composition fluctuations. The solid solution is very stable. Only a very limited fraction (never exceeding 1%) of nanometer-sized, bcc Fe particles appears after long-time isothermal anneals at suitable temperatures. A negative magnetoresistance was observed at room temperature in all examined samples. The observed effect is anhysteretic, isotropic, and quadratically dependent on magnetic field H and magnetization M. The signal scales with M rather than with H, indicating that it depends on the field-induced magnetic order of the Fe moments, as it does for conventional giant magnetoresistance in granular magnetic systems. This effect derives from spin-dependent scattering of conduction electrons from single Fe spins or very small Fe clusters. The scattering centers are almost uncorrelated at a distance of the order of the electronic mean free path (of the order of 1.5 nm, or a few atomic spacings, at RT).

Nuclear magnetic resonance investigations of the structure and magnetic properties of metallic multilayers and nanocomposites

As a probe of the short-range chemical and topological order, nuclear magnetic resonance (NMR) has proved useful to investigate the nanostructure of magnetic multilayers or granular systems and, in particular, to evaluate the nature, sharp or diffuse, of interfaces in such nanocomposites. These structural aspects are shortly reviewed in the paper. A larger emphasis is given to the magnetic properties that are accessed by the technique. As a first output of an NMR experiment in ferromagnets, the hyperfine field gives a direct insight on the local magnetization. Hence, for example, one can estimate the magnetization profile at a diffuse interface between a magnetic and nonmagnetic phase. In addition, NMR can probe selectively the magnetic anisotropy or exchange energy in different parts of a composite sample. Therefore NMR is a unique tool to investigate the correlation, at a local scale, between the nanostructure and the magnetic properties of a sample. For example, one can evidence the different magnetic hardness of the interface and bulk moments in multilayers, or of the magnetic clusters and alloyed regions in nanogranular alloys. Some relevant results are presented, which have been obtained in the course of investigations of Co-based multilayers, ultrathin films and granular systems.

Intergranule interaction in magnetic granular films

Magnetic granular films consist of nanoscale magnetic granules embedded in an insulator or in an immiscible metal. The advantage of granular films is that there exists abundant interface between magnetic granules and the matrix with unique microstructures. The physical properties in these systems can be tailored by adjusting the composition, volume fraction of constituent materials, and preparation conditions. In this paper, some results on domain observation in Co 35(SiO 2) 65 granular film and spin-wave resonance in FeSiO 2 granular film will be presented, which may be helpful to understand the intergranule interaction in magnetic granular systems.

Magnetic hysteresis based on dipolar interactions in granular magnetic systems

The magnetic hysteresis of granular magnetic systems is investigated in the high-temperature limit $(T\ensuremath{\gg}$ blocking temperature of magnetic nanoparticles). Measurements of magnetization curves have been performed at room temperature on various samples of granular bimetallic alloys of the family ${\mathrm{Cu}}_{100\ensuremath{-}x}{\mathrm{Co}}_{x} (x=5--20 \mathrm{at}.%)$ obtained in ribbon form by planar flow casting in a controlled atmosphere, and submitted to different thermal treatments. The loop amplitude and shape, which are functions of sample composition and thermal history, are studied taking advantage of a novel method of graphical representation, particularly apt to emphasize the features of thin, elongated loops. The hysteresis is explained in terms of the effect of magnetic interactions of the dipolar type among magnetic-metal particles, acting to hinder the response of the system of moments to isothermal changes of the applied field. Such a property is accounted for in a mean-field scheme, by introducing a memory term in the argument of the Langevin function which describes the anhysteretic behavior of an assembly of noninteracting superparamagnetic particles. The rms field arising from the cumulative effect of dipolar interactions is linked by the theory to a measurable quantity, the reduced remanence of a major symmetric hysteresis loop. The theory's self-consistence and adequacy have been properly tested at room temperature on all examined systems. The agreement with experimental results is always striking, indicating that at high temperatures the magnetic hysteresis of granular systems is dominated by interparticle, rather than single-particle, effects. Dipolar interactions seem to fully determine the magnetic hysteresis in the high-temperature limit for low Co content $(x<~10).$ For higher concentrations of magnetic metal, the experimental results indicate that additional hysteretic mechanisms have to be introduced.